As the function \(\varphi \)  is a diffeomorphism preserving the orientation of time, the dynamics of system (REF ) is topologically equivalent to system (REF ) [1]}. Therefore, we can conclude that there are conditions in the system parameter for which the predator and prey can coexist or both populations oscillate. This behaviour depends on the predation rate (\(q\) ) and the intrinsic growth rate of the predator (\(s\) ).
